CN1549207A - Filling method for closed zone - Google Patents
Filling method for closed zone Download PDFInfo
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- CN1549207A CN1549207A CNA031367097A CN03136709A CN1549207A CN 1549207 A CN1549207 A CN 1549207A CN A031367097 A CNA031367097 A CN A031367097A CN 03136709 A CN03136709 A CN 03136709A CN 1549207 A CN1549207 A CN 1549207A
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Abstract
The method of filling a closed area formed by one closed path via several vertexes includes the following steps: generating path chain list including several nodes for recording the vertexes and intermediate points in the closed path; generating filling array chain list according to the path chain list; filling the array chain list to record the filling line segments inside the closed path and with ends on the closed path; and finally filling the closed area based on the filling line segments.
Description
Technical field
The present invention relates to a kind of fill method of closed region, and be particularly related to a kind of method for quickly filling of closed region.
Background technology
Please refer to Fig. 1, it is depicted as the process flow diagram of traditional closed region fill method.At first, obtain the coordinate on the summit on the path, shown in step 110.These summits for example are the summits shown in the 2nd figure.Then, find out the minimum rectangle that comprises all summits, shown in step 120.Then, open up a zone in internal memory, regional corresponding (the corresponding pixel of byte) of the minimum rectangle that is distributed with the summit is shown in step 130.Then, in region of memory, with outside the closed region have a few, within the closed region have a few, the summit in path, hypotenuse (comprise vertical edges, do not comprise the summit) identify with different values with horizontal sides (not comprising the summit), shown in step 140.Then, point by point scanning line by line, according to the position of current point and current point the value that identified judge whether into filling the end points of line segment, shown in step 150.At last, fill this closed region according to the value of the end points of the filling line segment that obtains above, shown in step 160.
Forming closed path with one by 100 summits is example, and it is 100 * 100 (units: on zone pixel) that these summits are distributed in length and width.In the 3rd step of old algorithm, when judging that whether a point is the point of inside of closed region, the coordinate on all summits (totally 100 summits) on the coordinate (totally 100 * 100 points) of this point and the path need be compared, see whether it is the summit in path.Only this item just needs to judge approximately (100 * 100) * 100 time, promptly 1000000 times.Most of the time is consumed in such computing.In step 150, judge whether current point is when filling the end points of line segment, need judge that one by one operand is bigger to these 100 * 100 points.
In step 130, need in internal memory, open up a zone ((unit: pixel) regional corresponding that 100 * 100byte) is 100 * 100 with length and width that the summit is distributed.When the zone of summit distribution is very big, a large amount of memory headrooms will be taken.
Summary of the invention
In view of this, purpose of the present invention is exactly that a kind of method for quickly filling of closed region is being provided.
According to purpose of the present invention, a kind of fill method of closed region is proposed.The closed region is to be enclosed in the closed path that is formed by a plurality of summits.This method may further comprise the steps.At first, produce the path chained list.The path chained list comprises a plurality of nodes, and each node is in order to summit on the record closed path or a plurality of intermediate points between each summit on the closed path.Then, produce the filling array linked list according to the path chained list.Fill array linked list in order to write down a plurality of filling line segments, each two-end-point of filling line segment is positioned on the closed path, and these interstitial wire sections are positioned at the closed region.At last, fill line segment according to these and fill this closed region.
According to fill method of the present invention, have the following advantages: 1. reduce operand:
A. need not need all the pixel pointwises in the closed region are judged as classic method, and only the pixel on the closed path be judged, therefore can reduce operand.B. do not have complicated multiplication and division to calculate, mostly be simple numeric ratio greatly, therefore can reduce operand.2. reduce the demand of internal memory: classic method needs an internal memory, and is corresponding with all pixels of the minimum rectangle of surrounding all summits, therefore need expend more internal memory.And this method only needs the path chained list, fills array linked list etc., and the internal memory that need take is less.
Description of drawings
For above-mentioned purpose of the present invention, feature and advantage can be become apparent, a preferred embodiment cited below particularly, and cooperate appended graphicly, be described in detail below:
Fig. 1 is depicted as the process flow diagram of traditional closed region fill method.
Fig. 2 illustrates a plurality of summits distribution plan on the plane.
Fig. 3 illustrates the process flow diagram according to the fill method of a kind of closed region of the preferred embodiments of the present invention.
Fig. 4 A illustrates the process flow diagram of the line index on decision summit.
Fig. 4 B illustrates the process flow diagram of the dot mark on decision summit.
Fig. 4 C illustrates the method flow diagram of the end marker on decision summit.
Fig. 4 D and 4E illustrate the method flow diagram that produces the path chained list.
Fig. 5 A is the pixel synoptic diagram that path chained list P is linked.
Fig. 5 B is the content among the chained list P of path.
Fig. 6 A and 6B illustrate and produce the method flow diagram of filling array linked list.
Fig. 7 is the content according to the filling array linked list that flow process produced of 6A and 6B figure.
Fig. 8 illustrates the closed region synoptic diagram after the filling.
Embodiment
Fig. 2 illustrates a plurality of summits distribution plan on the plane.The coordinate of summit (0)～summit (10) is respectively (6,0), (2,4), (5,4), (0,8), (5,8), (5,12), (7,12), (7,8), (12,8), (7,4) and (10,4).Last summit (11) also is summit (0).These summits surround a closed path, closed path encloses one closed region.The following description will be that example explains with these summits of the 2nd figure.Fig. 3 illustrates the process flow diagram according to the fill method of a kind of closed region of preferred embodiment of the present invention.At first receive these summits, shown in step 300.Write down the coordinate on these summits in regular turn with the summit array, and last summit in path is first summit.Then, calculate all intermediate points between the summit on the closed path, and deposit these summits and intermediate point in path chained list (linked list) P according to the order of closed path, shown in step 400 according to these summits.Then, try to achieve filling array linked list G according to this path chained list P, shown in step 500.Fill array linked list G and promptly write down the point at two ends of the horizontal line section of required filling.Last foundation is filled array linked list G and is filled this closed region, shown in step 600.
In step 400, the method that produces path chained list P is described as follows.At first, determine the attribute on each summit, be shown in the process flow diagram of 4A figure to 4C figure.Then, calculate on the closed path all between the summit intermediate point and deposit these summits and intermediate point in path chained list P according to the order of closed path, be shown in the process flow diagram of 4D and 4E figure.
Each summit has ordinate x, horizontal ordinate y, and according to the summit different attributes is arranged with the relative position on other summit, represents with line index (flag) F1, dot mark Fp and end marker Fe.Current summit is with summit (r) expression, and last summit is with summit (r-1) expression, and one summit, back is represented with summit (r+1).If current summit (r) is first, just summit (0), then summit (r-1) is summit (10); In like manner, if current summit (r) is summit (11), then summit (r+1) is summit (1).R is a positive integer.
Fig. 4 A illustrates the process flow diagram of the line index on decision summit.Line index F1 determines to be level, vertical or inclination according to current summit with the formed line segment in last summit.At first, check whether the ordinate y (r) on current summit (r) equates with the ordinate y (r-1) of last summit (r-1), shown in step 310.If, represent that the current summit (r) and the line segment on last summit (r-1) they are level, then the line index F1 with current summit (r) is denoted as level, and shown in step 312, for example summit (2).Otherwise check whether the horizontal ordinate x (r) on current summit (r) equates with the horizontal ordinate x (r-1) of last summit (r-1), shown in step 314.If the line index F1 on then current summit (r) is denoted as vertically, shown in step 316, for example summit (5).If not, the horizontal ordinate x (r-1) with last summit (r-1) is different with ordinate y (r-1) respectively with ordinate y (r) for the horizontal ordinate x (r) on expression summit (r), then the line index F1 with current summit (r) is denoted as inclination, shown in step 318, for example summit (1).
Fig. 4 B illustrates the process flow diagram of the dot mark on decision summit.Dot mark Fp determines to be A type, C type, L1 type or L2 type according to current summit (r) with the relative position on last summit (r-1) and one summit, back (r+1).Whether the ordinate y (r) that at first checks current summit (r) is simultaneously greater than the ordinate y (r-1) of last summit (r-1) and the ordinate y (r+1) on one summit, back (r+1), shown in step 320.If the dot mark Fp on then current summit (r) is the A type, for example summit (0).If not, check that whether the ordinate y (r) on current summit (r) is simultaneously less than the ordinate y (r-1) of last summit (r-1) and the ordinate y (r+1) on one summit, back (r+1), shown in step 324.If the dot mark Fp on then current summit (r) is the A type, shown in step 322.If not, check that the ordinate y on current summit (r) is whether between the ordinate y (r+1) on ordinate y of last summit (r-1) (r-1) and one summit, back (r+1), shown in step 326.If the dot mark Fp on then current summit (r) is the C type, shown in step 328.If not, the ordinate of then representing current summit (r) is identical with the ordinate on last summit (r-1) or one summit, back (r+1).At this moment, check whether the ordinate y (r) on current summit (r) is identical with the ordinate y (r-1) of last summit (r-1), shown in step 330.If represent that then the current summit (r) and the line segment on last summit (r-1) are level, carry out step 332; Otherwise represent that the current summit (r) and the line segment on one summit, back (r+1) are levels, carry out step 334.In step 332, whether the horizontal ordinate x that checks current summit (r) is greater than the horizontal ordinate x of last summit (r-1).If then the dot mark Fp of summit (r) is the L2 type, shown in step 338, for example summit (2); If not, the dot mark Fp on then current summit (r) is the L1 type, shown in step 336.In step 334, whether the horizontal ordinate x (r) that checks current summit (r) is greater than the horizontal ordinate x (r+1) on one summit, back (r+1).If the dot mark Fp on then current summit (r) is the L2 type, shown in step 338; If not, the dot mark Fp on then current summit (r) is the L1 type, shown in step 336.
Fig. 4 C illustrates the method flow diagram of the end marker on decision summit.In step 340, check three conditions, if one of these three conditions are set up, represent that then the end marker Fe on summit (r) is true (step 342), otherwise the end marker Fe on expression summit (r) is pseudo-(step 344).First condition is: the ordinate y (r) of current summit (r) is less than the ordinate y (r+1) on one summit, back (r+1), and more than or equal to the ordinate y (r-1) of last summit (r-1).Second condition is: the ordinate y (r) of current summit (r) is less than the ordinate y (r-1) of last summit (r-1), and more than or equal to the ordinate y (r+1) on one summit, back (r+1).The 3rd condition is: the dot mark Fp of current summit (r) is A type or C type.If end marker Fe is true, expression summit (r) is the end points of filling line segment.Repeat the flow process shown in Fig. 4 A to 4C, tried to achieve its line index F1, dot mark Fp and end marker Fe up to all summits all.
Next all intermediate points between the summit on the closed path be to calculate, and these summits and intermediate point deposited in path chained list P according to the order of closed path.Fig. 4 D and 4E illustrate the method flow diagram that produces the path chained list.The order that determines to try to achieve the method for intermediate point and insert path chained list P according to the line index F1 of current summit (r).In step 350, judge whether the line index F1 on current summit (r) is level, if execution in step 352 then.In step 354, whether the line index F1 that judges current summit (r) is vertical, if execution in step 356～362 then.If step 350 all denys that the line index F1 on then current summit (r) is for tilting execution in step 363～368 with 354 judged result.
If the line index F1 on current summit (r) is a level, then current summit (r) inserted the end (step 352) of path chained list P, and execution in step 370 is to judge whether current summit (r) inserts path chained list P.That is to say, summit (r) and summit (r-1) if the line segment level, then its intermediate point is not recorded in path chained list P.
If the line index F1 on current summit (r) is vertical, at first judge in step 356: whether the ordinate y (r) of current summit (r) is greater than the ordinate y (r-1) of last summit (r-1), just summit (r) on the summit below of (r-1), and the difference of the ordinate y (r) of current summit (r) and the ordinate y (r-1) on last summit (r-1) just has intermediate point between summit (r) and summit (r-1) greater than 2.If then in regular turn the intermediate point between summit (r-1) to summit (r) is inserted path chained list P, the just order (step 358) that increases progressively according to ordinate; Otherwise enter step 360.Judge in step 360: whether the ordinate y (r) of current summit (r) is less than the ordinate y (r-1) of last summit (r-1), just summit (r) on the summit top of (r-1), and the difference of the ordinate y (r) of current summit (r) and the ordinate y (r-1) on last summit (r-1) just has intermediate point between summit (r) and summit (r-1) greater than 2.If then in regular turn the intermediate point between summit (r-1) to summit (r) is inserted path chained list P, the just order (step 358) of successively decreasing according to ordinate; Otherwise enter step 370.
If the line index F1 on current summit (r) is for tilting, at first judge in step 363: whether the ordinate y (r) of current summit (r) is greater than the ordinate y (r-1) of last summit (r-1), just summit (r) on the summit below of (r-1), and the difference of the ordinate y (r) of current summit (r) and the ordinate y (r-1) on last summit (r-1) just has intermediate point between summit (r) and summit (r-1) greater than 2.If then in regular turn the intermediate point between summit (r-1) to summit (r) is inserted path chained list P, the just order (step 364) that increases progressively according to ordinate; Otherwise enter step 366.These intermediate points are to try to achieve with the equation of line on summit (r-1) according to summit (r).Judge in step 366: whether the ordinate y (r) of current summit (r) is less than the ordinate y (r-1) of last summit (r-1), just summit (r) on the summit top of (r-1), and the difference of the ordinate y (r) of current summit (r) and the ordinate y (r-1) on last summit (r-1) just has intermediate point between summit (r) and summit (r-1) greater than 2.If then in regular turn the intermediate point between summit (r-1) to summit (r) is inserted path chained list P, the just order (step 368) of successively decreasing according to ordinate; Otherwise enter step 370.These intermediate points are to try to achieve with the equation of line on summit (r-1) according to summit (r).In step 370,, then summit (r) inserted the end of path chained list P if current summit (r) is not last summit, path.Repeat the method shown in 4D and the 4E figure, up to all summits and intermediate point deposit path chained list P in according to the order of closed path all.
Fig. 5 A is the pixel synoptic diagram that path chained list P is linked.Except the summit, the intermediate point between the summit is also obtained, and two summits on the horizontal line are the intermediate points that do not write down therebetween, is not write down intermediate point between summit (1) and summit (2) for example.Fig. 5 B is the content among the chained list P of path.Each element among the chained list P of path promptly corresponds to a summit or an intermediate point, and each element includes horizontal ordinate x, ordinate y, index index, dot mark Fp, end marker Fe and index next.Index index is in order to write down the order on each summit, and the index index of intermediate point then is-1, and for example the index index of summit (0) is 0.The dot mark Fp of intermediate point is all the C type.If end marker Fe is true, then in the chained list P of path, represent with 1, otherwise with 0 expression.Index next is in order to point to next node.Each element promptly links in regular turn according to the order of closed path.
To elaborate to producing the method for filling array linked list in the step 500 again.At first fill array linked list G according to one of the height h application of closed path.In this example, h is 13.Each array of filling array linked list G is corresponding chained list, and a chained list is the pixel that corresponds to same row.G[0 for example] be the pixel of corresponding ordinate y=0, G[1] be the pixel of corresponding ordinate y=1 ..., G[12] be the pixel of corresponding ordinate y=12.In addition, G[13] chained list pointed then is used for writing down horizontal lines all on the closed path.Each G[] chained list pointed comprises two end points of filling line segment.Can fill the closed region that these summits surround according to filling line segment.Fig. 6 A and 6B illustrate and produce the method flow diagram of filling array linked list G.All summits and intermediate point on the closed path, each node of path chained list P just, all Using such method is inserted and is filled array linked list G in regular turn.Check at first whether node is intermediate point (step 512), if then this node is write corresponding filling array linked list G[y according to its ordinate y] (step 514), represent that if not this node is the summit.In step 520, check whether the dot mark Fp on this summit is the A type, if then write corresponding filling array linked list G[y according to its ordinate y] twice.If because of dot mark Fp A type, for example be the summit A among the 2nd figure, represent that same horizontal line has only this point, be same point so write this Origin And Destination of filling line segment of twice expression.Whether the dot mark Fp that comes then to check the summit again is that L1 or L2 type (step 530) are if represent that this summit is to be positioned on the horizontal line section of closed path, carry out step 532, otherwise carry out step 540.In step 532, this summit write fills array linked list G[h], then will fill array linked list G[h] in the end marker Fe on this summit make very (step 534) into.Whether the end marker Fe that checks this summit among the chained list P of path then is true (step 536), if then this summit is write corresponding filling array linked list G[y according to its ordinate y] (step 538).If the dot mark Fp on summit is the C type, then this summit is write corresponding filling array linked list G[y according to its ordinate y] (step 540).
Fig. 7 illustrates the content according to the filling array linked list that flow process produced of Fig. 6 A and 6B.Fill array linked list G[0] be the filling line segment (6,0) (6,0) that corresponds to y=0, fill array linked list G[1] be the filling line segment (5,1) (7,1) that corresponds to y=1, fill array linked list G[2] be the filling line segment (4,2) (8,2) that corresponds to y=2, fill array linked list G[3] be the filling line segment (3,3) (9,3) that corresponds to y=3, ..., fill array linked list G[11] be the filling line segment (5,11) (7,11) that corresponds to y=11.Fill array linked list G[12] be the filling line segment that corresponds to y=12, there is no the filling line segment herein.Fill array linked list G[h], G[13 just], be horizontal chained list, be used for writing down horizontal line all on the closed path (2,4) (5,4), (0,8) (5,8), (5,12) (7,12) (7,8) (12,8) and (7,4) (10,4).
Last according to filling array linked list G filling closed region.Please refer to Fig. 8, it is depicted as the closed region synoptic diagram after the filling.Foundation is filled the end points coordinate that array linked list G can obtain filling line segment, and each end points of filling line segment is connected with specific color, with all filling line segments and painted the finishing of horizontal line section on the closed path, has also just finished the filling of closed region.
The fill method of the disclosed closed region of the above embodiment of the present invention has the following advantages:
1. reduction operand:
A. need not need all the pixel pointwises in the closed region are judged as classic method, and only the pixel on the closed path be judged, therefore can reduce operand.
B. do not have complicated multiplication and division to calculate, mostly be simple numeric ratio greatly, therefore can reduce operand.
2. reduce the demand of internal memory: classic method needs an internal memory, and is corresponding with all pixels of the minimum rectangle of surrounding all summits, therefore need expend more internal memory.And this method only needs the path chained list, fills array linked list etc., and the internal memory that need take is less.
In sum, though the present invention is open according to above preferred embodiment, yet be not in order to limit the present invention; any those skilled in the art; without departing from the spirit and scope of the present invention, can change or improve, so protection scope of the present invention is as the criterion so that claims are described.
Claims (22)
1. the fill method of a closed region, this closed region is to be enclosed in the closed path that is formed by a plurality of summits, and according to the order that is positioned on the closed path, respectively this summit has last summit and one summit, back, and this method comprises:
Produce the path chained list, this path chained list comprises a plurality of nodes, and respectively this node is in order to write down respectively one of a plurality of intermediate points between these summits on these summits and this closed path on this closed path;
Produce the filling array linked list according to this path chained list, in order to write down a plurality of filling line segments, each these two-end-point of filling line segments is to be positioned on this closed path, and these interstitial wire sections are positioned at this closed region; And
Fill line segment according to these and fill this closed region.
2. fill method as claimed in claim 1, the step that wherein produces this path chained list comprises:
A1. determine the line index on this summit to be level, vertically to reach one of inclination according to this last summit and the relative position on this summit;
A2. if having intermediate point between this summit and this last summit, then this line index according to this summit inserts this path chained list with the intermediate point between this summit and this last summit; And
A3. if this summit is not this last summit on this closed path, then this summit is inserted the end of this path chained list.
3. fill method as claimed in claim 2 wherein in step a2, if this line index on this summit is a level, does not then write down these intermediate points between this summit and this last summit.
4. fill method as claimed in claim 2, wherein in step a2, if this line index on this summit is vertical, and the ordinate on this summit is greater than the ordinate on this last summit, and the order that these intermediate points between this last summit and this summit are increased progressively according to its ordinate is inserted the tail of this path chained list.
5. fill method as claimed in claim 2, wherein in step a2, if this line index on this summit is vertical, and this ordinate on this summit is less than the ordinate on this last summit, and between this summit and this last summit intermediate point is arranged, the order that these intermediate points between this last summit and this summit are successively decreased according to its ordinate is inserted the tail of this path chained list.
6. fill method as claimed in claim 2, wherein in step a2, if this line index on this summit is for tilting, and the ordinate on this summit is greater than the ordinate on this last summit, then will this last summit and this summit between the order that increases progressively according to its ordinate of these intermediate points insert the tail of this path chained list.
7. fill method as claimed in claim 2, wherein in step a2, if this line index on this summit is for tilting, and the ordinate on this summit is less than the ordinate on this last summit, then will this last summit and this summit between these intermediate points order of successively decreasing according to its ordinate insert the tail of this path chained list.
8. fill method as claimed in claim 7, wherein in step a2, these intermediate points get by the linear equation of this summit with this last summit in regular turn.
9. fill method as claimed in claim 2 is wherein in step a1, if this horizontal ordinate on this summit equates that with this horizontal ordinate on last this summit then this line index on this summit is a level.
10. fill method as claimed in claim 2 is wherein in step a1, if this ordinate on this summit equates that with this ordinate on this last summit then this line index on this this summit is vertical.
11. fill method as claimed in claim 2, wherein in step a1, if this horizontal ordinate on this summit does not wait with this horizontal ordinate on last this summit, and this ordinate on this ordinate on this summit and this last summit do not wait, and then this line index on this summit is inclination.
12. fill method as claimed in claim 1, wherein this filling array linked list has a plurality of line segment chained lists, and respectively this line segment chained list is filled one of line segment in order to write down these.
13. fill method as claimed in claim 12, wherein these filling line segments are levels.
14. fill method as claimed in claim 13, wherein in producing this step of filling array linked list, if this node of this path chained list is this intermediate point, then the ordinate according to this intermediate point is recorded to this corresponding line segment chained list with this intermediate point.
15. fill method as claimed in claim 13, wherein in producing this step of filling array linked list, if this node of this path chained list is this summit, and this ordinate on this summit is greater than this ordinate on this last summit and this ordinate on this one summit, back, and then the ordinate according to this summit is recorded in this corresponding line segment chained list twice with this summit.
16. fill method as claimed in claim 13, wherein in producing this step of filling array linked list, if this node of this path chained list is this summit, and this ordinate on this summit is less than this ordinate on this last summit and this ordinate on this one summit, back, and then the ordinate according to this summit is recorded in this corresponding line segment chained list twice with this summit.
17. fill method as claimed in claim 13, wherein this filling array linked list more comprises horizontal chained list, in order to write down at least one horizontal line section on this closed path.
18. fill method as claimed in claim 17, wherein in producing this step of filling array linked list, if this node of this path chained list is this summit, and this summit forms this horizontal line section with one of this last summit and this one summit, back, then this summit is recorded to this horizontal chained list of this filling array linked list.
19. fill method as claimed in claim 17, in producing this step of filling array linked list, if this node of this path chained list is this summit, and this summit forms this horizontal line section with this last summit, then according to the ordinate on this summit this summit is recorded to this line segment chained list of correspondence.
20. fill method as claimed in claim 13, in producing this step of filling array linked list, if this node of this path chained list is this summit, and this ordinate on this summit is between the ordinate on the ordinate on this last summit (r-1) and this one summit, back, and then the ordinate according to this summit is recorded to this corresponding line segment chained list with this summit.
21. fill method as claimed in claim 13 in the step of filling this closed region, is distinctly to fill these filling line segments that these line segment chained lists are write down wherein.
22. fill method as claimed in claim 17 in the step of filling this closed region, is distinctly to fill these filling line segments that these line segment chained lists are write down wherein, and this at least one horizontal line section that this horizontal chained list write down.
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| WO2010034267A1 (en) * | 2008-09-28 | 2010-04-01 | 北大方正集团有限公司 | Method and apparatus for simplifying complicated path |
| CN101276334B (en) * | 2007-03-29 | 2011-04-06 | 上海新跃仪表厂 | Linked list implementing method for quickly searching data |
| CN108096835A (en) * | 2018-01-26 | 2018-06-01 | 珠海金山网络游戏科技有限公司 | The area filling method and device of a kind of map |
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| CN1154959C (en) * | 2001-02-15 | 2004-06-23 | 英业达股份有限公司 | System and method for serging graphics and characters |
| CN1177287C (en) * | 2001-04-18 | 2004-11-24 | 无敌科技(西安)有限公司 | Automatic format setting method for palm-type browser |
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|---|---|---|---|---|
| CN101276334B (en) * | 2007-03-29 | 2011-04-06 | 上海新跃仪表厂 | Linked list implementing method for quickly searching data |
| WO2010034267A1 (en) * | 2008-09-28 | 2010-04-01 | 北大方正集团有限公司 | Method and apparatus for simplifying complicated path |
| US8773440B2 (en) | 2008-09-28 | 2014-07-08 | Peking University Founder Group Co., Ltd | Method and device for simplifying a complex path |
| CN108096835A (en) * | 2018-01-26 | 2018-06-01 | 珠海金山网络游戏科技有限公司 | The area filling method and device of a kind of map |
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